As \(\eta (\cdot )\)  is admissible, the constructed kernel
\(L_{2n}(x,y),\)  called the needlet kernel (or localized polynomial
kernel) [1]} henceforth, is positive definite. We
will show that so defined kernel function \(L_{2n}(x,y)\) , deduces
the \(l^q\)  regularization learning whose learning rate is independent
of the choice of \(q\) . To this end, we first show several useful
properties of the needlet kernel.
